 15.1: Melissa said that (a 1 3)2 5 a2 1 9. Do you agree with Melissa? Jus...
 15.2: If a trinomial is multiplied by a binomial, how many times must you...
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 15.7: In 323, perform the indicated operations and write the result in si...
 15.8: In 323, perform the indicated operations and write the result in si...
 15.9: In 323, perform the indicated operations and write the result in si...
 15.10: In 323, perform the indicated operations and write the result in si...
 15.11: In 323, perform the indicated operations and write the result in si...
 15.12: In 323, perform the indicated operations and write the result in si...
 15.13: In 323, perform the indicated operations and write the result in si...
 15.14: In 323, perform the indicated operations and write the result in si...
 15.15: In 323, perform the indicated operations and write the result in si...
 15.16: In 323, perform the indicated operations and write the result in si...
 15.17: In 323, perform the indicated operations and write the result in si...
 15.18: In 323, perform the indicated operations and write the result in si...
 15.19: In 323, perform the indicated operations and write the result in si...
 15.20: In 323, perform the indicated operations and write the result in si...
 15.21: In 323, perform the indicated operations and write the result in si...
 15.22: In 323, perform the indicated operations and write the result in si...
 15.23: In 323, perform the indicated operations and write the result in si...
 15.24: In 2429, solve for the variable and check. Each solution is an inte...
 15.25: In 2429, solve for the variable and check. Each solution is an inte...
 15.26: In 2429, solve for the variable and check. Each solution is an inte...
 15.27: In 2429, solve for the variable and check. Each solution is an inte...
 15.28: In 2429, solve for the variable and check. Each solution is an inte...
 15.29: In 2429, solve for the variable and check. Each solution is an inte...
 15.30: The length of a rectangle is 4 more than twice the width, x. Expres...
 15.31: The length of the longer leg, a, of a right triangle is 1 centimete...
Solutions for Chapter 15: Multiplying Polynomials
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 15: Multiplying Polynomials
Get Full SolutionsChapter 15: Multiplying Polynomials includes 31 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Since 31 problems in chapter 15: Multiplying Polynomials have been answered, more than 29329 students have viewed full stepbystep solutions from this chapter.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Outer product uv T
= column times row = rank one matrix.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.